$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 5x - 2$ and $ BC = 8x - 11$ Find $AC$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {5x - 2} = {8x - 11}$ Solve for $x$ $ -3x = -9$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 5({3}) - 2$ $ BC = 8({3}) - 11$ $ AB = 15 - 2$ $ BC = 24 - 11$ $ AB = 13$ $ BC = 13$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {13} + {13}$ $ AC = 26$